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A Discursively Oriented Conceptualization of Mathematical Problem Solving

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Problem Solving in Mathematics Instruction and Teacher Professional Development

Part of the book series: Research in Mathematics Education ((RME))

Abstract

This chapter suggests a discursively oriented conceptualization of mathematical problem solving and then illustrates the conceptualization by putting it in use for rethinking results of two past studies on problem solving. In the first study, a practice of developing and using heuristic discourse was facilitated in two eighth-grade classes during a 5-month period. This practice positively affected problem-solving heuristic literacy and aptitudes of those students who were identified as “weak” at the beginning of the intervention. In the second study, effort was made to incorporate aesthetic discourse in problem-solving discussions in three middle-school classes during 8-month period. The effort resulted in gradual change of sociomathematical norms and development of positive attitude to mathematics in one of the participating classes. The chapter concludes by discussion of the promise of the proposed conceptualization for practice.

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Change history

  • 01 February 2020

    The published version of this book included multiple errors in code listings throughout the book. These code listings have now been corrected and text has been updated.

Notes

  1. 1.

    For the sake of precision, it should be acknowledged that more than one discursive perspective exists (e.g., Sfard, 2013). They all share focus on the sociocultural nature of teaching and learning and on discourse, but they differ in some of their ontological premises. Sfard (2013) suggests considering a spectrum of the discursive perspectives, within which she locates her own perspective, (i.e., a perspecitve that unifies the divide between public and private discourses), as a “strong” discursive perspective. The term discursive perspective is used in this chapter broadly, which means that it does not necessarily refer to the “strong” discursive perspective. For this reason and for the sake of clarity, the to-be-offered conceptualization of mathematical problem solving is called discursively oriented rather than discursive.

  2. 2.

    This subsection is based on the abridged and reorganized descriptions of the study that appear in Koichu, Berman, and Moore 2007a, 2007b).

  3. 3.

    The whole interview is analyzed in depth in Koichu and Leron (2015).

  4. 4.

    Following Goldin (2009), we mean by an emotionally safe instructional environment, “…an environment in which mistakes, false starts, wrong answers, problem solving impasses, and criticism of one another’s ideas are not avoided or downplayed, but come to be regarded as the productive outcomes of bold, courageous, praiseworthy, inventive effort” (Goldin, 2009, p. 191).

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Acknowledgments

I would like to thank Michal Tabach, Anna Sfard, and the anonymous reviewers for valuable comments that helped me to shape the argument presented in this chapter.

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Authors and Affiliations

  1. Department of Science Teaching, Weizmann Institute of Science, Rehovot, Israel

    Boris Koichu

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  1. Boris Koichu
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  1. Departamento de Ingeniería Matemática, University of Chile, Santiago, Chile

    Patricio Felmer

  2. Faculty of Education, Simon Fraser University, Burnaby, BC, Canada

    Peter Liljedahl

  3. Department of Science Teaching, Weizmann Institute of Science, Rehovot, Israel

    Boris Koichu

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Koichu, B. (2019). A Discursively Oriented Conceptualization of Mathematical Problem Solving. In: Felmer, P., Liljedahl, P., Koichu, B. (eds) Problem Solving in Mathematics Instruction and Teacher Professional Development. Research in Mathematics Education. Springer, Cham. https://doi.org/10.1007/978-3-030-29215-7_3

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